1. HEP 2003 Europhysics Conference in Aachen, Germany Study of Inclusive Jets Production in ep Interactions at HERA Mónica Luisa Vázquez Acosta Universidad Autónoma de Madrid On behalf of the ZEUS & H1 Collaborations

2. The HERA collider provides a unique laboratory for the study of the hadronic final state Jet physics at HERA • Jet data are very precise at high transverse energy where the experimental uncertainties and non-perturbative effects are small. This allows • Precision tests of perturbative QCD • Constrains on proton and photon parton distribution functions • Study the size of the theoretical uncertainties for further improvements • Extraction ofQCD parameters where the uncertainties are small • Study of subprocessesproportional to asor higher powers • Explore the low Q2 transition region where non-perturbative effects become important

3. HERA Kinematics • Negative squared4-momentum transfer • Bjorkenscaling variable • Inelasticity • Deep Inelastic Scattering: Neutral Current: • Total hadronic centre-of-mass energy Charged Current: • Photoproduction:

4. Inclusive Jet Photoproduction at HERA • In photoproduction the photon has low virtuality, at HERA Q2 ~ 10-3 GeV2 •  the high transverse energy jets provide a hard scale • High ET jet production is described up to O(a aS) in the SM by Resolved g is hadron-like Direct gis point-like Inclusive jet production does not restrict the phase space of the second jet  reduced theoretical uncertainties in the NLO QCD predictions  the information of the event kinematics is reduced

5. Inclusive Jet Cross Sections in PhotoproductionZEUS Collaboration - hep-ex/0212064 • Cross sections for jets with Good agreement of NLO QCD calculation with the measured cross section over 5 orders of magnitude Small theoretical uncertainties • uncertainty due to missing higher orders in the perturbative series ~10% • photon and proton PDFs ~ 5% Theoretical calculation from Klasen, Kleinwort and Kramer - Eur. Phys. J. Direct C 2 (1998) 2

6. Measurement of as in PhotoproductionZEUS Collaboration - hep-ex/0212064 • as(MZ) values determined from a QCD fit to ds/dETjet in different ETjet regions • Small experimental uncertainties • Theoretical error dominates • Consistent with recent determination of Bethke Running of as in a single measurement A c2-fit to all the Etjet regions gives a value of aS(MZ) of: Bethke: hep-ex/0211012

7. Scaling Violations in PhotoproductionZEUS Collaboration - hep-ex/0212064 Scaling hypothesis:the scaled jet invariant cross section averaged over as a function of should be independent of Wgp • Theoretical uncertainties reduced • Scaling violation due to: parton evolution and running of as • First observation of scaling violations • in jet photoproduction Effectivelyequivalentto running with two different beam energies NLO QCD calculations are consistent with the data

8. Inclusive Jet Cross Sections in PHPH1 Collaboration - hep-ex/0302034 • Agreement with NLO QCDvery good • All predictions obtained using different proton(MRST99,CTEQ5) and photon(GRV,AFG)PDFs agree with the data Theoretical calculation from Frixione, Ridolfi - Nucl. Phys. B 507 (1997) 315

9. Comparison of gp with ppH1 Collaboration - hep-ex/0302034 Scaled cross section: independent of energy up to scaling violations xT < 0.2 ]shape similar forgp and pp ]resolved photon ~ hadron xT > 0.2 ]gp harder than ppspectrum • enhanced quark density in the resolved photon w.r.t. a hadron • dominance of direct ]point-like photon ]Confirmation of the dual nature of the photon

10. Born QCD-Compton Jets in Deep Inelastic Scattering O (aS) is described in the SM by Jet production in DIS Breit Frame • Jets with high ET in the Breit frame: • Supress Born contribution (the current quark has no ET) • Lowest order contributions QCD-Compton and boson-gluon fusion • Directly sensitive to QCD subprocesses at O (aS)

11. Inclusive jets in NC DIS at low Q2H1 Collaboration - hep-ex/0206029 Backward Central Forward • At large virtualities Q2  125 GeV2 data agrees • well with NLO QCD predictions • At low virtualities discrepancies are seen and • are studied in more detail • Good agreement of NLO QCD with • data in backward and central regions • Large NLO corrections for low ET and in the forward region: NLO/LO~5 NLO predictionsbelow data for ET < 20 GeV in the forward region Discrepancy

12. Inclusive jets in NC DIS: forward regionH1 Collaboration - hep-ex/0206029 Forward region: 1.5 < hlab < 2.8 NLO predictionsup to 50% lower than datawhere NLO corrections are largest

13. Azimuthal asymmetry of jets in NC DIS ZEUS Collaboration - hep-ex/0210064 No jet cuts in the laboratory frame • Distribution of the azimuthal angle in the Breit frame • between the lepton scattering plane and the plane • defined by the jet and the incoming proton direction • LO pQCD predicts for NC DIS at Q2 << MZ2 • In g*q→qg the outgoing g(q) preferentially appears at f=0(p) • In g*g→qq the f dependence is dominated by the cos2f term • For an inclusive jet measurement: • Smallexperimental and theoretical uncertainties • NLO QCD calculations describe the measurements very well Normalised cross section

14. Azimuthal asymmetry of jets in NC DIS ZEUS Collaboration - hep-ex/0210064 To quantify the asymmetry and the dependence with Q2  a fit was performed to the data and the QCD calculation using the functional form • f1 is consistent with 0 • f2 decreases with Q2 Normalised inclusive jet cross section folded about p • The asymmetry is predicted to decrease as Q2 increases • due to the progressive decline of the g*g→qq process • NLO QCDdescribes the data well • LO QCD predicts a larger asymmetry at low Q2 Precise test of pQCD prediction for the azimuthal asymmetry

15. Inclusive jets in Charged Current DIS ZEUS Collaboration - hep-ex/0306018 • Test flavour changing electroweak theory and QCD in one type of events • Analysis peformed in the laboratory frame 1. NLO QCD calculations (MEPJET) 2. Matrix elements+parton showers (ARIADNE MC) have been compared to the data Mirkes and Zeppenfeld, Phys. Lett. B380 (1996) 205 Lönnblad, Z. Phys. C 65 (1995) 285 Both the NLO QCD and MC calculations describe well the data

16. Jet Substructure of inclusive jets in CC DIS ZEUS Collaboration - hep-ex/0306018 Mean subjet multiplicity NC CC The measurement is sensitive to the value of aS(MZ) A c2-fit to the region Etjet > 25 GeV where the parton-to-hadron corrections are <10% gives a value of aS(MZ) of: QCD does not distinguish if W (CC) or g (NC) is exchanged

17. Summary and Outlook • HERA is now producing a wealth of precision jet data at high ETin NC and CC deep inelastic scattering, photoproduction and the transition region. • Many extractions of the QCD coupling constant aS with a precision competitive with the world average. The running behaviour of aS is clearly seen. • At high ETjetin inclusive jet cross sections, theoretical uncertainties are small and the theoretical predictions are able to reproduce cross sections over many orders of magnitude. • At lower Q2theoretical uncertainties are dominant theoretical developments are needed. • Experimental precision and coverage of data is now very good time to include the HERA jet data in global PDF fits.